Write equations for and graph ratio situations. Define independent and dependent variables.
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This lesson brings together several concepts and skills that students have worked on throughout the year, such as tables of equivalent values (6.RP.3), writing equations (6.EE.1), plotting points (6.NS.8), and determining values in ratio relationships (6.RP.3). The novelty is not in any one specific concept or skill but rather in how they interact and represent one another in new ways. For example, after studying equations, students can now use an equation to represent how two quantities in a ratio situation are related to one another, they can show this visually in the coordinate plane, and analyze the relationship to draw conclusions (MP.4).
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 2 (benefit from worked examples). Anchor Problem 1 introduces new vocabulary to students; if live discussion or reflection were possible, it may support students in understanding these new terms. Find more guidance on adapting our math curriculum for remote learning here.
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A recipe for sugar cookies calls for 1 cup of sugar for every 2 cups of flour.
Sugar (cups) | 1 | 8 | |||
Flour (cups) | 6 | 10 | 20 |
Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below.
Time (hours) | Miles Walked |
1 | |
2 | 6 |
12 | |
5 |
Walk-A-Thon 1, accessed on Feb. 28, 2018, 4:21 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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To make green paint, a paint store combines blue and yellow paint in a specific ratio, as shown in the table below.
Blue Paint (pints) | Yellow Paint (pints) |
2 | 3 |
4 | 6 |
6 | 9 |
8 | 12 |
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